Structural materials that feature hierarchical architectures (e.g., fractals) display remarkable mechanical properties. Menger sponge is one of the fractal geometries defined in Mathematics and made up of a unit cube with three orthogonal cavities. The precise fractal dimensions are fabricated using 3D printing. Experiments and simulations are conducted on the structure under uniaxial compression. The effect of increasing the levels of orthogonal cavities of the Menger sponge structure as well as the changing shape of the cavity are studied. The results show an interesting correlation between mechanical properties and the effective density of the structure. Multiple levels of hierarchy are analyzed in terms of different cavity shapes. These comparisons suggest that hierarchical structures are used to obtain better performance with a lower effective density of the resulting structures. Damage initiation for the different cavity shapes shows how each of the cavity shapes behaves under compressive loading. Herein, it is discerned how hierarchical architecture is used to access the unique properties of structures, providing insight into the role of design in regulating the mechanical properties of such mechanical structures. The result of acoustic investigation shows that it is a better absorber as compared with commercial sponge in the low‐frequency regime.
Plates with periodic cavities show excellent vibration attenuation characteristics. This behavior can be attributed to the presence of frequency bandgaps on account of interference between the incident wave and the reflected wave from the cavities. The present work investigates the vibration attenuation/bandgap characteristics of plates with varying shapes of periodic cavities, such as square, circular, vertical rectangle, and horizontal rectangle, through experiments and simulation. Vibration responses of different periodic plates have been studied by carrying out frequency sweep on a vibration shaker. The investigation has been restricted to flexural vibrations of the plates, which are the predominant mode of vibration in many practical vibration scenarios. The frequency bandgaps, observed through the experiment, have been compared with the numerical simulation by harmonic analysis and by carrying out dispersion analysis on a unit cell of the periodic structure using Floquet–Bloch theory. Dispersion curves of the periodic plates yielded bandgaps, which were observed to be in agreement with the bandgaps from the experiment. The effect of variation in the aspect ratio of the cavities, that is length-to-width ratio, on the bandgaps has also been examined. It has been demonstrated that by suitable selection of the shape/size of the periodic cavity, desired vibration attenuation bandgaps can be realized for a 2-dimensional structure.
Vibration attenuation in acoustic-metamaterial plates assembled from a periodic arrangement of unit cells with a cavity containing local resonator system is presented. Each cell incorporates a base aluminum plate with vertical rectangle-shaped cavities containing a viscoelastic membrane supporting a mass forming a local resonator system. These acoustic-metamaterial structures exhibit stop-band behavior due to Bragg scattering and local resonance. Floquet–Bloch approach and eigenvalue analysis is used to identify the stop bands for metamaterial unit cells. The dispersion analysis predictions are validated experimentally by studying the vibration responses of different acoustic-metamaterial plates excited by an electrodynamic shaker over a frequency range of 8−4000 Hz. The attenuation regions observed in the finite element simulation results have been compared to that of the experiments. The obtained results show the potential of FE simulation to predict the metamaterial plate attenuation with reasonably good accuracy. The viscoelastic material properties also affect the attenuation region, as observed while comparing experimental results for different viscoelastic materials. These results show the effectiveness of acoustic-metamaterial plates to provide broadband vibration attenuation.
An incompressible Navier-Stokes solver has been developed to analyze the three-dimensional viscous flow around a pair of square cylinders at a low Reynolds number (Re = 100) at various arrangements. A semi-implicit finite difference scheme was employed on a staggered grid, which facilitated the easier application of boundary conditions while achieving satisfactory accuracy and stability. A third-order upwind (Kawamura-Kuwahara) scheme was applied to discretize the convective terms and a second-order central difference scheme to discretize the diffusive terms. Time integration was performed using a second-order accurate Adams-Bashforth scheme. An iterative pressurevelocity correction was used to obtain a divergence-free velocity field. Aspects of the flow such as vorticity profiles, the time evolution of lift and drag coefficients, and three-dimensionality appearance were studied. Three-dimensional characteristics ceased to appear in a tandem arrangement, irrespective of the gap ratio. In contrast, the side by side arrangement showed a clear threedimensional transition in the flow when analyzing the vortex structures. Further investigations carried out for staggered arrangement keeping the center to center distance constant and varying the stagger angle (α) reveal that the * Author to whom any correspondence should be addressed.
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